Rigid body: gears physical animation
To improve the accuracy of the Rigid Body simulation you can increase the Steps setting in the Rigid Body World settings of the Scene properties. This defaults to 60 - larger values breaks the simulation into smaller steps at the expense of taking longer to calculate - try increasing by a factor of 10 or more. Smaller steps results in better collision and a more stable simulation.

However, that isn't actually the problem with your animation. The problem is actually due to the meshes themselves - the normals are flipped and pointing 'into' the object rather than 'out'. This means that the collision becomes confused and Blender is behaving as if the objects are actually caught within each other which results in the 'stuck' animation as one cog attempts to turn.

The solution is to simply select each cog in turn, enter Edit mode (Tab), select all (A until all is selected) and press Ctrl+N to Make Normals Consistent. This tells Blender to recalculate the normals, by default pointing them 'out' of the object.

Once the normals were corrected I didn't need to make any other changes on your file for the cogs to animate.